// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_ANGLEAXIS_H
#define EIGEN_ANGLEAXIS_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
  *
  * \class AngleAxis
  *
  * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
  *
  * \param _Scalar the scalar type, i.e., the type of the coefficients.
  *
  * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized.
  *
  * The following two typedefs are provided for convenience:
  * \li \c AngleAxisf for \c float
  * \li \c AngleAxisd for \c double
  *
  * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
  * mimic Euler-angles. Here is an example:
  * \include AngleAxis_mimic_euler.cpp
  * Output: \verbinclude AngleAxis_mimic_euler.out
  *
  * \note This class is not aimed to be used to store a rotation transformation,
  * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
  * and transformation objects.
  *
  * \sa class Quaternion, class Transform, MatrixBase::UnitX()
  */

namespace internal {
    template <typename _Scalar> struct traits<AngleAxis<_Scalar>>
    {
        typedef _Scalar Scalar;
    };
}  // namespace internal

template <typename _Scalar> class AngleAxis : public RotationBase<AngleAxis<_Scalar>, 3>
{
    typedef RotationBase<AngleAxis<_Scalar>, 3> Base;

public:
    using Base::operator*;

    enum
    {
        Dim = 3
    };
    /** the scalar type of the coefficients */
    typedef _Scalar Scalar;
    typedef Matrix<Scalar, 3, 3> Matrix3;
    typedef Matrix<Scalar, 3, 1> Vector3;
    typedef Quaternion<Scalar> QuaternionType;

protected:
    Vector3 m_axis;
    Scalar m_angle;

public:
    /** Default constructor without initialization. */
    EIGEN_DEVICE_FUNC AngleAxis() {}
    /** Constructs and initialize the angle-axis rotation from an \a angle in radian
    * and an \a axis which \b must \b be \b normalized.
    *
    * \warning If the \a axis vector is not normalized, then the angle-axis object
    *          represents an invalid rotation. */
    template <typename Derived> EIGEN_DEVICE_FUNC inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
    /** Constructs and initialize the angle-axis rotation from a quaternion \a q.
    * This function implicitly normalizes the quaternion \a q.
    */
    template <typename QuatDerived> EIGEN_DEVICE_FUNC inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
    /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
    template <typename Derived> EIGEN_DEVICE_FUNC inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }

    /** \returns the value of the rotation angle in radian */
    EIGEN_DEVICE_FUNC Scalar angle() const { return m_angle; }
    /** \returns a read-write reference to the stored angle in radian */
    EIGEN_DEVICE_FUNC Scalar& angle() { return m_angle; }

    /** \returns the rotation axis */
    EIGEN_DEVICE_FUNC const Vector3& axis() const { return m_axis; }
    /** \returns a read-write reference to the stored rotation axis.
    *
    * \warning The rotation axis must remain a \b unit vector.
    */
    EIGEN_DEVICE_FUNC Vector3& axis() { return m_axis; }

    /** Concatenates two rotations */
    EIGEN_DEVICE_FUNC inline QuaternionType operator*(const AngleAxis& other) const { return QuaternionType(*this) * QuaternionType(other); }

    /** Concatenates two rotations */
    EIGEN_DEVICE_FUNC inline QuaternionType operator*(const QuaternionType& other) const { return QuaternionType(*this) * other; }

    /** Concatenates two rotations */
    friend EIGEN_DEVICE_FUNC inline QuaternionType operator*(const QuaternionType& a, const AngleAxis& b) { return a * QuaternionType(b); }

    /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
    EIGEN_DEVICE_FUNC AngleAxis inverse() const { return AngleAxis(-m_angle, m_axis); }

    template <class QuatDerived> EIGEN_DEVICE_FUNC AngleAxis& operator=(const QuaternionBase<QuatDerived>& q);
    template <typename Derived> EIGEN_DEVICE_FUNC AngleAxis& operator=(const MatrixBase<Derived>& m);

    template <typename Derived> EIGEN_DEVICE_FUNC AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
    EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix(void) const;

    /** \returns \c *this with scalar type casted to \a NewScalarType
    *
    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
    * then this function smartly returns a const reference to \c *this.
    */
    template <typename NewScalarType> EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AngleAxis, AngleAxis<NewScalarType>>::type cast() const
    {
        return typename internal::cast_return_type<AngleAxis, AngleAxis<NewScalarType>>::type(*this);
    }

    /** Copy constructor with scalar type conversion */
    template <typename OtherScalarType> EIGEN_DEVICE_FUNC inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
    {
        m_axis = other.axis().template cast<Scalar>();
        m_angle = Scalar(other.angle());
    }

    EIGEN_DEVICE_FUNC static inline const AngleAxis Identity() { return AngleAxis(Scalar(0), Vector3::UnitX()); }

    /** \returns \c true if \c *this is approximately equal to \a other, within the precision
    * determined by \a prec.
    *
    * \sa MatrixBase::isApprox() */
    EIGEN_DEVICE_FUNC bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
    {
        return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle, other.m_angle, prec);
    }
};

/** \ingroup Geometry_Module
  * single precision angle-axis type */
typedef AngleAxis<float> AngleAxisf;
/** \ingroup Geometry_Module
  * double precision angle-axis type */
typedef AngleAxis<double> AngleAxisd;

/** Set \c *this from a \b unit quaternion.
  *
  * The resulting axis is normalized, and the computed angle is in the [0,pi] range.
  * 
  * This function implicitly normalizes the quaternion \a q.
  */
template <typename Scalar>
template <typename QuatDerived>
EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
{
    EIGEN_USING_STD(atan2)
    EIGEN_USING_STD(abs)
    Scalar n = q.vec().norm();
    if (n < NumTraits<Scalar>::epsilon())
        n = q.vec().stableNorm();

    if (n != Scalar(0))
    {
        m_angle = Scalar(2) * atan2(n, abs(q.w()));
        if (q.w() < Scalar(0))
            n = -n;
        m_axis = q.vec() / n;
    }
    else
    {
        m_angle = Scalar(0);
        m_axis << Scalar(1), Scalar(0), Scalar(0);
    }
    return *this;
}

/** Set \c *this from a 3x3 rotation matrix \a mat.
  */
template <typename Scalar> template <typename Derived> EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
{
    // Since a direct conversion would not be really faster,
    // let's use the robust Quaternion implementation:
    return *this = QuaternionType(mat);
}

/**
* \brief Sets \c *this from a 3x3 rotation matrix.
**/
template <typename Scalar>
template <typename Derived>
EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
{
    return *this = QuaternionType(mat);
}

/** Constructs and \returns an equivalent 3x3 rotation matrix.
  */
template <typename Scalar> typename AngleAxis<Scalar>::Matrix3 EIGEN_DEVICE_FUNC AngleAxis<Scalar>::toRotationMatrix(void) const
{
    EIGEN_USING_STD(sin)
    EIGEN_USING_STD(cos)
    Matrix3 res;
    Vector3 sin_axis = sin(m_angle) * m_axis;
    Scalar c = cos(m_angle);
    Vector3 cos1_axis = (Scalar(1) - c) * m_axis;

    Scalar tmp;
    tmp = cos1_axis.x() * m_axis.y();
    res.coeffRef(0, 1) = tmp - sin_axis.z();
    res.coeffRef(1, 0) = tmp + sin_axis.z();

    tmp = cos1_axis.x() * m_axis.z();
    res.coeffRef(0, 2) = tmp + sin_axis.y();
    res.coeffRef(2, 0) = tmp - sin_axis.y();

    tmp = cos1_axis.y() * m_axis.z();
    res.coeffRef(1, 2) = tmp - sin_axis.x();
    res.coeffRef(2, 1) = tmp + sin_axis.x();

    res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c;

    return res;
}

}  // end namespace Eigen

#endif  // EIGEN_ANGLEAXIS_H
